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JEE Main & Advanced Mathematics Conic Sections Question Bank Hyperbola

  • question_answer
    The line \[3x-4y=5\]is a tangent to the hyperbola\[{{x}^{2}}-4{{y}^{2}}=5\]. The point of contact is

    A)            (3, 1)                                         

    B)            (2, 1/4)

    C)            (1, 3)                                         

    D)            None of these

    Correct Answer: A

    Solution :

               Suppose point of contact be (h, k), then tangent is \[hx-4ky-5=0\equiv 3x-4y-5=0\] or \[h=3,\,k=1\] Hence the point of contact is (3, 1).


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